Michał Tadeusiewicz and Stanisław Hałgas
The purpose of this paper is to develop a method for finding all the DC solutions in nonlinear circuits with the thermal constraint.
Abstract
Purpose
The purpose of this paper is to develop a method for finding all the DC solutions in nonlinear circuits with the thermal constraint.
Design/methodology/approach
The proposed approach employs an algorithm for finding all the DC solutions without thermal constraint, including a new contraction and elimination method, an efficient method for tracing characteristics expressing voltages and power in terms of temperature, and electrical analog of the chip thermal behavior.
Findings
The paper brings a method that guarantees finding all the DC solutions, considering thermal behavior of the chip, in mid‐scale practical transistor circuits.
Originality/value
A new contraction and elimination method, being the core of the algorithm for finding all the DC solutions, is proposed. An approach enabling us to consider a feedback between the power dissipated inside the chip and the temperature, which affects the circuit parameters and consequently the solutions is developed.
Details
Keywords
Michał Tadeusiewicz and Stanisław Hałgas
Developing an efficient second‐order integration method of transient analysis of nonlinear dynamic circuits which overcomes the main drawback of the trapezoidal rule.
Abstract
Purpose
Developing an efficient second‐order integration method of transient analysis of nonlinear dynamic circuits which overcomes the main drawback of the trapezoidal rule.
Design/methodology/approach
Dynamic circuits including transistors and operational amplifiers are considered. A new family of two‐step, second‐order numerical integration algorithms has been developed using a polynomial approximation.
Findings
The algorithms have been worked out which are implicit, A‐stable and they depend on a parameter which is allowed to be changed during the computation process according to a proposed strategy. Also the variable step‐size formula has been derived enabling us to eliminate a restarting procedure. The method has been implemented and tested using several representative circuits. It has been compared, both theoretically and via numerical examples, with the alternative well known algorithms: the trapezoidal rule and the backward differentiation formula of order two.
Research limitation/implications
The algorithms developed in the paper are two‐step and second‐order, consequently the step size cannot be too large and the algorithms are not L‐stable.
Originality/value
A new family of two‐step implicit integration algorithms is developed. It can be useful for the analysis and design of electronic circuits.